Search Results: more affection from my boyfriend

So I just moved to England (from Canada) to be with my boyfriend. Everything has been just as amazing as it always has been, even better because we're not long distance anymore. But yesterday everything changed... I got up to change a song on his phone and a message from a girl popped up. I've never gone through his phone before but this message was very sexual and I was confused so clicked it. So I open the chat up and firstly see that he's had it locked (I could only see because I clicked the notification) and see my worst nightmare... All these sexual messages and pictures sent between my boyfriend and this girl he had met on the dating app we got (for fun to see our rating) These detailed descriptions of what my boyfriend would do to her in person. It made me nauseous and I ran to the bathroom as I thought I would throw up. I confronted him about it. He said he was sorry and he wouldn't do it again (he deleted the app that moment) but agreed he wouldn't have told me if I didn't find out. Later on I asked him to explain it more and in summary he said:- He was talking to another girl months ago in this way.- He craves the power of making girls want him and liked the rush lying to me gave him, but has never and would never have sex with them, and;- He stopped seeing a girl friend of his because he felt that they might have done stuff if they continued seeing eachother. I feel absolutely disgusted that he did this two times and part of the reason was some sick rush it gave him... I feel dumb and weak and more upset than I could have imagined, I left my job, family, and friends for him... On the other hand, I love him so much, we have plans for the future and besides this, our relationship is very healthy- full of respect, affection, romance, and fun. He said he will do whatever it takes to make it right (even go to counselling) but my trust is broken. I don't just want to stay because it would hurt leaving, but don't want to leave if we can fix this and move on.

Something I've noticed about myself is that I have a hard time settling down. I tend to fixate on one person, start a relationship with them, and get bored with it a few months later. It's during this period of boredom that I usually find myself interested in flirting with other people, while I still have extreme affection for the person I'm dating.
My last relationship had a few periods like this, and though I still felt completely in love with my boyfriend, I always wanted more. I hate this about myself, and I certainly can't stand being single, but sometimes relationships can be a bit slow and it drives me crazy.
I won't deny I enjoy attention, and as someone with a lot of anxiety concerning myself and how others see me, I will constantly search for attention and approval when I feel like it's lacking from my current relationship. So I guess my biggest question is, if I have no intentions of leaving the person I am with currently, is it still bad to engage in harmless flirting during relationship "lulls"?